An advanced hyperheuristic approach for the home health care scheduling problem with time window in deterministic and uncertain environments

In the last two decades, Home Health Care (HHC) services have garnered substantial attention from global researchers and practitioners. These services face significant challenges related to strategic, tactical, and operational decisions that must be solved for enhancing their efficiency and quality. Notably, researchers have focused significantly on the scheduling and routing aspects, recognizing their potential to enhance patient satisfaction, safety, and cost-effectiveness for both patients and HHC companies. Recent studies have highlighted the stochastic nature of these services, including random service and travel times, that may affect the scheduling and routing components. Nonetheless, a significant portion of recent research predominantly focuses on the deterministic version of the problem, disregarding its fundamental stochastic nature as emphasized by feedback from HHC companies. Within this context, we propose a two-stage mixed integer mathematical formulation to address the Home Health Care Scheduling and Routing Problem (HHCSRP), encompassing stochastic demand, service, and travel times. Given the inherent Nondeterministic Polynomial (NP)-hardness of these scheduling and routing problems, we introduce a hyperheuristic approach based on a TS metaheuristic and Variable Neighborhood Search (VNS) heuristic. Extensive experiments validate the effectiveness of our proposed modeling and solving approaches, outperforming similar methods across various metrics. Notably, our stochastic model exhibits superior performance in terms of parameters like the number of patients served within time windows and computational time required to achieve optimal solutions. This study thus contributes a valuable decision support system for Home Health Care companies, empowering them to make informed decisions and construct robust schedules for their caregivers.